<p>The dissolved gas analysis is a commonly used method for evaluating the condition of power transformers. The Duval Pentagon method, based on the Duval Triangle method, improves fault identification accuracy by introducing H₂ and C₂H₆ as additional gases. This method calculates the centroid of the pattern formed by the concentrations of characteristic gases to determine the type of fault. Currently, research on the Duval Pentagon method is limited in China, and its capability to differentiate between faults, such as partial discharge and overheating, remains to be validated. This paper first investigates the performance of the Duval Pentagon method in distinguishing between various transformer faults, revealing that the method is less effective in differentiating discharge-related faults. To improve the method's ability to identify discharge faults, the diagnostic performance of different characteristic gases for discharge-related faults is evaluated. The weights of the characteristic gases are determined using the normalized silhouette coefficient method, and a weighted Duval Pentagon fault diagnosis approach is proposed. Finally, case tests are conducted. The results show that the optimized method significantly enhances the differentiation capability for combinations of partial discharge with low-energy discharge, partial discharge with high-energy discharge, and low-energy discharge with high-energy discharge, with improvements of 3.9 times, 2.3 times, and 3.0 times, respectively. The fault identification accuracy for the 3 types of discharge is increased to 85, 75, and 75%, respectively.</p>